Simulating the electrophysiology of discretely-coupled cardiac cells - - PowerPoint PPT Presentation

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Simulating the electrophysiology of discretely-coupled cardiac cells - - PowerPoint PPT Presentation

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Simulating the electrophysiology of discretely-coupled cardiac cells in a multi-domain formulation C. Houston, E. Dupont, R.A. Chowdhury, N.S. Peters, S.J. Sherwin, C.D. Cantwell ElectroCardioMaths Programme, Imperial College London Nektar++

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Simulating the electrophysiology of discretely-coupled cardiac cells in a multi-domain formulation

  • C. Houston, E. Dupont, R.A. Chowdhury, N.S. Peters, S.J. Sherwin, C.D. Cantwell

ElectroCardioMaths Programme, Imperial College London Nektar++ Workshop, 11 June 2019

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Outline

  • Introduction to cardiac electrophysiology
  • Discrete-cell model in Nektar++
  • Initial validation results
  • Conclusions & Future work
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Outline

  • Introduction to cardiac electrophysiology
  • Discrete-cell model in Nektar++
  • Initial validation results
  • Conclusions & Future work
  • Introduction to cardiac electrophysiology
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What’s in a heartbeat?

AC Guyton and JE Hall. Textbook of Medical Physiology. 1996. S Rohr. Role of gap junctions in the propagation of cardiac action potential. Cardiovasc Res. 2004. N Sperelakis, K McConnell. Electric field interactions between closely abutting excitable cells. IEEE engineering in medicine and biology magazine. 2002 Jan;21(1):77-89.

JHeuser, 2005.

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What’s in a heartbeat?

Adapted from Guyton and Hall, 1996. Fig 9-2.

AC Guyton and JE Hall. Textbook of Medical Physiology. 1996. S Rohr. Role of gap junctions in the propagation of cardiac action potential. Cardiovasc Res. 2004. N Sperelakis, K McConnell. Electric field interactions between closely abutting excitable cells. IEEE engineering in medicine and biology magazine. 2002 Jan;21(1):77-89.

JHeuser, 2005.

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What’s in a heartbeat?

Adapted from Guyton and Hall, 1996. Fig 9-2.

AC Guyton and JE Hall. Textbook of Medical Physiology. 1996. S Rohr. Role of gap junctions in the propagation of cardiac action potential. Cardiovasc Res. 2004. N Sperelakis, K McConnell. Electric field interactions between closely abutting excitable cells. IEEE engineering in medicine and biology magazine. 2002 Jan;21(1):77-89.

JHeuser, 2005. Rohr, 2004. Fig 3. Sperelakis, 2002..

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Pathmanathan et al, 2018.

P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology

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Pathmanathan et al, 2018.

P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology

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Cantwell et al, 2015. Pathmanathan et al, 2018.

P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology

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Cantwell et al, 2015. Pathmanathan et al, 2018.

P Pathmanathan and RA Gray. Validation and trustworthiness of multiscale models of cardiac electrophysiology. Front Physiol. 2018. J Keener and J Sneyd. Mathematical Physiology II: Systems Physiology. Springer Science & Business Media. 2009. CD Cantwell et al. Nektar++: An open-source spectral/element framework. Comput Phys Commun. 2015.

Modelling cardiac electrophysiology

  • Steep spatial gradient at wavefront.
  • Stiffness of ODE cell model.
  • Geometric complexity.
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Organ-scale rotational activity

Cantwell CD et al. High-order spectral/hp element discretisation for reaction–diffusion problems on surfaces: Application to cardiac electrophysiology. Journal of computational physics. 2014 Jan 15;257:813-29.

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Biological preparation

Houston C et al. Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line. Journal of molecular and cellular cardiology. 2018 Jun 1;119:155-64.

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Cell-scale rotational activity

Houston C et al. Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line. Journal of molecular and cellular cardiology. 2018 Jun 1;119:155-64.

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We aim to develop the first biophysically-validated and morphologically-accurate discrete cell model for action potential propagation in cardiac cell monolayers.

Hypothesis & Aims

We hypothesise that conduction features at a cellular level are a key factor in the initiation and perpetuation

  • f re-entrant arrhythmias and fibrillation in vivo.
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Outline

  • Introduction to cardiac electrophysiology
  • Discrete-cell model in Nektar++
  • Initial validation results
  • Conclusions & Future work
  • Introduction to cardiac electrophysiology
  • Discrete-cell model in Nektar++
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Idealised model for cable of cells

... cell i cell i+1 ... GJ G

M M

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Idealised model for cable of cells

... cell i cell i+1 ... GJ G

M M

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... cell i cell i+1 ... GJ G

M M

Idealised model for cable of cells

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... cell i cell i+1 ... GJ G

M M

Idealised model for cable of cells

(L + Λ)û = f

L = discrete Laplacian Λ = interface coupling

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Interfaces Extracellular space Cells

L

Multi-domain global matrix system

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Interfaces Extracellular space Cells

L + Λ

Multi-domain global matrix system

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Outline

  • Introduction to cardiac electrophysiology
  • Discrete-cell model in Nektar++
  • Initial validation results
  • Conclusions & Future work
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0.05 0.1 0.15

  • 0.3
  • 0.2
  • 0.1

Length (cm ) Voltage (AU)

Intracellular Extracellular Transm em brane

λg=0.11cm

Steady-state solution for fixed potential at cable end

0.05 0.1 0.15 .3 .2 .1

Length (cm )

Intracellular Extracellular Transm em brane 0.05 0.1 0.15 .3 .2 .1

Length (cm )

Intracellular Extracellular Transm em brane

λg=0.07cm λg=0.09cm

Increased gap junction resistance leads to greater proportion of decay across gap junctions.

λg Rg

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0.05 0.1 0.15

  • 0.1
  • 0.05

0.05 0.1

Length (cm ) Transm em brane voltage (AU)

Analytic Sim ulation

λg Rg

Steady-state solution for current injected into cable

0.05 0.1 0.15 .1 05 05 0.1

Length (cm )

Analytic Sim ulation 0.05 0.1 0.15 .1 05 05 0.1

Length (cm )

Analytic Sim ulation

λg=0.11cm λg=0.07cm λg=0.09cm

‘Speed bumps’ at gap junctions as current redistributes for path of least resistance.

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Outline

  • Introduction to cardiac electrophysiology
  • Discrete-cell model in Nektar++
  • Initial validation results
  • Conclusions & Future work
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Conclusions

We have constructed a multi-domain formulation within the Nektar++ framework to solve steady-state solutions for cell- level conduction in cardiac electrophysiology. The framework reproduces known analytical solutions for a cable of connected cardiac cells.

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What’s next?

Incorporate time-dependent features at interfaces (i.e. cell model ODEs). Direct biophysical validation of our model with one-to-one matching biological preparations. Prediction of effects of changes to intercellular coupling on cell-scale conduction patterns.

  • Generalise multi-domain support in the library.
  • Parallelise solving in separate domains.
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Supervisors Dr Chris Cantwell Dr Rasheda A Chowdhury Prof Spencer Sherwin Prof Nicholas S Peters Dr Emmanuel Dupont (past) ElectroCardioMaths Group Dr David Pitcher Dr Fu Siong Ng PhD Assessors Prof Denis Doorly Prof Cesare Terraciano

Acknowledgements

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0.05 0.1 0.15

  • 0.3
  • 0.2
  • 0.1

Length (cm) Voltage (AU)

0.05 0.1 0.15

Length (cm)

0.05 0.1 0.15

Length (cm)

A B C

Intracellular potential Extracellular potential Transm em brane potential

0.2 0.4 0.6 0.8 1

  • 1
  • 0.5

0.5 1

Length, cm Transmembrane potential, AU

A B

0.56 0.58 0.6 0.62 0.64

  • 0.1
  • 0.05

0.05 0.1

Length, cm Transmembrane potential, AU

Analytical Simulation

1D steady-state solutions

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(L + Λ)û = f

... cell i cell i+1 ... GJ G

M M

L = discrete Laplacian Λ = interface coupling

Idealised model for cable of cells

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C Houston et al. Characterisation of re-entrant circuit (or rotational activity) in vitro using the HL1-6 myocyte cell line. J Mol Cell Cardio. 2018. B Handa et al. Analytical approaches for myocardial fibrillation signals. Comput. Biol. Med. 2018.

Conduction block/slowing algorithm